p(t) = aßtB-1 %3D 68. TH a>0 to B> 0 (a (a) Show that p(t) is constant if ß = 1. (b) Find p'(t). Argue that p'(t) > 0 if ß > 1, thus producing an increasing hazard rate. Argue that p'(t) < 0 if B < 1, thus producing a decreasing (b) %3D (c hazard rate. 03. A system has eight components connected as shown in Fig. 4.22. Section 69. Pr 10 201TEITATZ C CONTINUOUS DISTRIBUTIONS 151 .85 4. .80 8 .93 .98 .94 .999 .80 .75 п IV III V FIGURE 4.22 (a) Find the reliability of each of the parallel assemblies. (b) Find the system reliability. (c) Suppose that assembly II is replaced by two identical components in par- allel, each with reliability .98. What is the reliability of the new assembly? (d) What is the new system reliability after making the change suggested in part (c)? (e) Make changes analogous to that of part (c) in each of the remaining sin- gle component assemblies. Compute the new system reliability. 66. A system consists of two independent components connected in series. The life span of the first component follows a Weibull distribution with a = .006
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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